The development of advanced nanocomposite materials requires innovative strategies to overcome stability challenges in lightweight structures. In this study, an analytical model based on Higher-Order Shear Deformation Theory (HSDT) and Hamilton’s principle is employed to investigate the buckling behavior of functionally graded carbon nanotube (CNT)-reinforced composite beams with varying porosity distributions. Three CNT dispersion patterns (uniform, X-type, and O-type) and five porosity types (uniform, symmetric-1, symmetric-2, asymmetric-1, and asymmetric-2) are examined. The results reveal that X-CNT distribution combined with symmetric-2 porosity significantly enhances critical buckling loads—with improvements of up to 20.2% compared to uniform porosity cases. The slenderness ratio (L/h) and porosity volume fraction are also found to strongly influence the structural stability. The proposed model shows excellent agreement with existing literature, validating its accuracy. The key contribution of this work lies in providing, for the first time, a comprehensive parametric study combining multiple porosity profiles and CNT distribution types to optimize buckling resistance. These findings offer valuable insights for the design of high-performance, lightweight structural components in aerospace, mechanical, and civil engineering applications.
ZhangHGaoCLiH, et al.Analysis of functionally graded carbon nanotube-reinforced composite structures: a review. Nanotechnol Rev2020; 9(1): 1408–1426.
2.
ŞimşekM. Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nucl Eng Des2010; 240(4): 697–705.
3.
ReissnerE. The effect of transverse shear deformation on the bending of elastic plates. J Appl Mech1945; 12(2): A68–A77.
4.
HussainMAsgharSKhadimallahMA, et al.Effect of dimensionless nonlocal parameter: vibration of double-walled CNTs. Comput Concr2022; 30(4): 269–276.
5.
TahirGAtifBMAbdelwahhabK, et al.Analytical investigation on the buckling and free vibration of porous laminated FG-CNTRC plates. Vojnotehnički glasnik2024; 72(3): 1242–1271.
6.
IijimaSIchihashiT. Single-shell carbon nanotubes of 1-nm diameter. Nature1993; 363(6430): 603–605.
7.
ZhangHGaoCLiH, et al.Analysis of functionally graded carbon nanotube-reinforced composite structures: a review. Nanotechnol Rev2020; 9(1): 1408–1426.
8.
GrygorowiczMMagnuckiKMalinowskiM. Elastic buckling of a sandwich beam with variable mechanical properties of the core. Thin-Walled Struct2015; 87: 127–132.
9.
ShafieiNMousaviAGhadiriM. On size-dependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams. Int J Eng Sci2016; 106: 42–56.
10.
ChenDYangJKitipornchaiS. Free and forced vibrations of shear deformable functionally graded porous beams. Int J Mech Sci2016; 108: 14–22.
11.
WuHLYangJKitipornchaiS. Nonlinear vibration of functionally graded carbon nanotube-reinforced composite beams with geometric imperfections. Compos B Eng2016; 90: 86–96.
12.
WattanasakulpongNUngbhakornV. Analytical solutions for bending, buckling and vibration responses of CNT-reinforced composite beams resting on elastic foundation. Comput Mater Sci2013; 71: 201–208.
13.
YangJChenDKitipornchaiS. Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method. Compos Struct2018; 193: 281–294.
14.
YangJChenDKitipornchaiS. (Same as above). Compos Struct2018; 193: 281–294.
15.
BaratiMRShahverdiH. Forced vibration of porous functionally graded nanoplates under uniform dynamic load using general nonlocal stress–strain gradient theory. J Vib Control2018; 24(20): 4700–4715.
16.
KitipornchaiSChenDYangJ. Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets. Mater Des2017; 116: 656–665.
17.
BenahmedAFahsiBBenzairA, et al.Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation. Struct Eng Mech2019; 69(4): 457–466.
18.
YangZWuHYangJ, et al.Nonlinear forced vibration and dynamic buckling of FG graphene-reinforced porous arches under impulsive loading. Thin-Walled Struct2022; 181: 110059.
19.
GafourYHamidiABenahmedA, et al.Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle. Advances in Nano Research2020; 8(1): 37–47.
20.
ZhangZYangQJinC. Axisymmetric vibration analysis of a sandwich porous plate in thermal environment rested on Kerr foundation. Steel Compos Struct2022; 43(5): 581–592.
21.
AlsubaieAMAl-OstaMAlfaqihI, et al.Influences of porosity distributions on bending and buckling behaviour of functionally graded carbon nanotube-reinforced composite beam. Comput Concr2024; 34(2): 179–193.
22.
BenahmedARakrakKSi TayebT, et al. Impact of Winkler–Pasternak foundation parameters on the buckling behavior of composite plates reinforced with FG-CNT in a parabolic distribution. J Compos Mater. 2024; 59: 1–14.
23.
BahramiMAFeliS. Synergistic influence of MWCNTs/RGO on low-velocity impact response and mechanical properties of carbon fiber/epoxy composite. Proc Inst Mech Eng, Part N: Journal of Nanomaterials, Nanoengineering and Nanosystems2025; 239(1-2): 81–93.
24.
GayenD. Thermo-elastic buckling and free vibration behavior of functionally graded beams with various materials gradation laws. Int J Adv Des Manuf Technol2024; 19(7): 5397–5416.
25.
GayenD. Thermo-elastic static behavior of functionally graded shafts with different material gradation patterns. Int J Mech Mater Des. 2024; 12: 8963–8978.
26.
OnvaniDJafariADehkordiMB. Carrera unified formulation for bending and free vibration analysis of sandwich plate with FG-CNT faces considering the both soft and stiff cores. Mech Adv Mater Struct2022; 29(27): 6718–6732.
27.
YasMHSamadiN. Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation. Int J Pres Ves Pip2012; 98: 119–128.
28.
BalubaidMRamadyAMahmoudSR, et al.Energy harvesting estimation from vibration of chopped fiber rod-reinforced microbeams with piezoelectric patch based on five parameter-surface-strain gradient beam model. Int J Struct Stabil Dynam2024.
29.
AbdelillahBZidourMZerroukiR, et al.Influence of porosity variations on the flexural response of FG-CNT composite beams resting on Winkler, Pasternak, and Kerr foundations. J Compos Mater2025. Online ahead of print.
30.
PangMZhouSMHuBL, et al.Free vibration analysis of a bidirectional functionally graded carbon nanotube reinforced composite beam. J Appl Mech Tech Phys2023; 64(5): 878–889.
31.
SekkakMZerroukiRZidourM, et al.Static analysis of nonlinear FG-CNT reinforced nano-composite beam resting on Winkler/Pasternak foundation. Advances in Nano Research2024; 16(5): 509.
32.
ZerroukiRKarasAZidourM. Critical buckling analyses of nonlinear FG-CNT reinforced nano-composite beam. Advances in nano research2020; 9(3): 211–220.
33.
ZhouOFlemingRMMurphyDW, et al.Defects in carbon nanostructures. Science1994; 263(5154): 1744–1747.
34.
ZerroukiRZidourMTounsiA, et al.Buckling behavior of nonlinear FG-CNT reinforced nanocomposite beam reposed on Winkler/Pasternak foundation. Comput Concr2024; 34(3): 297.
35.
TagraraSHBenachourABouiadjraMB, et al.On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams. Steel Compos Struct2015; 19(5): 1259–1277.
